What is the Greatest Common Factor of 23985 and 24000?

Greatest common factor (GCF) of 23985 and 24000 is 15.

GCF(23985,24000) = 15

We will now calculate the prime factors of 23985 and 24000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23985 and 24000.

How to find the GCF of 23985 and 24000?

We will first find the prime factorization of 23985 and 24000. After we will calculate the factors of 23985 and 24000 and find the biggest common factor number .

Step-1: Prime Factorization of 23985

Prime factors of 23985 are 3, 5, 13, 41. Prime factorization of 23985 in exponential form is:

23985 = 3² × 5¹ × 13¹ × 41¹

Step-2: Prime Factorization of 24000

Prime factors of 24000 are 2, 3, 5. Prime factorization of 24000 in exponential form is:

24000 = 2⁶ × 3¹ × 5³

Step-3: Factors of 23985

List of positive integer factors of 23985 that divides 23985 without a remainder.

1, 3, 5, 9, 13, 15, 39, 41, 45, 65, 117, 123, 195, 205, 369, 533, 585, 615, 1599, 1845, 2665, 4797, 7995

Step-4: Factors of 24000

List of positive integer factors of 24000 that divides 23985 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 125, 150, 160, 192, 200, 240, 250, 300, 320, 375, 400, 480, 500, 600, 750, 800, 960, 1000, 1200, 1500, 1600, 2000, 2400, 3000, 4000, 4800, 6000, 8000, 12000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23985 and 24000. The biggest common factor number is the GCF number.
So the greatest common factor 23985 and 24000 is 15.

Also check out the Least Common Multiple of 23985 and 24000